Graphene oxides are promising materials for novel electronic devices or anchoring of the active sites for catalytic applications. Here we focus on understanding the atomic oxygen (AO) binding and mobility on different regions of graphene (Gr) on Ru(0001). Differences in the Gr/Ru lattices result in the superstructure, which offers an array of distinct adsorption sites. We employ scanning tunneling microscopy and density functional theory to map out the chemical identity and stability of prepared AO functionalities in different Gr regions. The AO diffusion is utilized to establish that in the regions that are close to the metal substrate the terminally bonded enolate groups are strongly preferred over bridge-bonded epoxy groups. No oxygen species are observed on the graphene regions that are far from the underlying Ru, indicating their low relative stability. This study provides a clear fundamental basis for understanding the local structural, electronic factors and C-Ru bond strengthening/weakening processes that affect the stability of enolate and epoxy species.